, Volume 11, Issue 3, pp 175-184
Date: 17 Nov 2006

Some things couples always wanted to know about stable matchings (but were afraid to ask)

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In this note we study the National Resident Matching Program (NRMP) algorithm in the US market for physicians. We report on two problems that concern the presence of couples, a feature explicitly incorporated in the new NRMP algorithm (cf. Roth and Peranson in Am Econ Rev 89:748–780, 1999). First, we show that the new NRMP algorithm may not find an existing stable matching, even when couples’ preferences are ‘responsive’, i.e., when Gale and Shapley’s (Am Math Monthly 69:9–15, 1962) deferred acceptance algorithm (on which the old NRMP algorithm is based) is applicable. Second, we demonstrate that the new NRMP algorithm may also be anipulated by couples acting as singles.